Singular Value Decomposition
Performs singular value decomposition on a general matrix.
| \(\hspace{60px} A\hspace{50px}=\hspace{50px}U\hspace{110px}W\hspace{110px} V^{t}\\ \\ \normalsize{\left[\begin{array}\\ a_{\small 11}& a_{\small 12}& \cdots& a_{\small 1j}\\ a_{\small 21}& a_{\small 22}& \cdots& a_{\small 2j}\\ \vdots& \vdots& \ddots& \vdots\\a_{\small i1}& a_{\small i2}& \cdots& a_{\small ij}\\\end{array}\right]} ={\left[\begin{array}\\ u_{\small 11}& u_{\small 12}& \cdots& u_{\small 1j}\\ u_{\small 21}& u_{\small 22}& \cdots& u_{\small 2j}\\ \vdots& \vdots& \ddots& \vdots\\u_{\small i1}& u_{\small i2}& \cdots& u_{\small ij}\\\end{array}\right]} {\left[\begin{array}\\ w_{\small 11}& 0& \cdots& 0\\ 0& w_{\small 22}& \cdots& 0\\ \vdots& \vdots& \ddots& \vdots\\0&0& \cdots& w_{\small jj}\\\end{array}\right]} {\left[\begin{array}\\ v_{\small 11}& v_{\small 21}& \cdots& v_{\small j1}\\ v_{\small 12}& v_{\small 22}& \cdots& v_{\small j2}\\ \vdots& \vdots& \ddots& \vdots\\v_{\small 1j}& v_{\small 2j}& \cdots& v_{\small jj}\\\end{array}\right]}\\ \) |
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